Hi there. Well, I have some doubts about this exercise, I think I've solved it, but I wanted your opinion, which always help. So, it says:
There is no general method for solving the homogeneous general equation of second order
But if we already know a solution , then we always can find a second solution linearly independent
Demonstrate that this functions form a basis for the space of solutions of the differential equation (1).
So, what I did is simple. I know that if the solution is linearly independent, then the Wronskian must be zero. So, I just made the calculus for the wronskian:
Is this right?